Page 166 - Essentials of physical chemistry

128 Essentials of Physical Chemistry

Then the vapor pressure is most likely related to the fraction of molecules with no nearest neighbors
(gas-like) and perhaps related to the fraction of dimers and free molecules; Kier [12] found
2
log P (mmHg) ¼ 24:30f 0 þ 15:64f 1 ; R ¼ 0:997:

Again, for the isothermal compressibility they found a relationship in terms of the cluster fractions.

1 qV 6 2
(10 =bar) ¼ 79:60 43:61f 2 39:57f 3 30:32f 4 ; R ¼ 0:991:
b ¼ k ¼
V qP
T
The dielectric constant of water can also be fitted to
2
e ¼ 178:88f 1 þ 55:84; R ¼ 0:994,
and finally it is also possible to fit the viscosity of water using only the f 4 fraction as with
2
h(cP) ¼ 1:439f 4 þ 0:202; R ¼ 0:965:
On one hand it should be clear that the coefficients of these excellent correlations offer little
interpretation in terms of fundamental constants but on the other hand the sum of these several
correlations offers credibility to the overall CA parameters used here. We can see that some
properties depend strongly on f 1 , which suggests dependence on dimer structure dominance while
the vapor pressure does sensibly depend on molecules with no neighbors, which is this model’s way
of indicating a gas. At the very least, this body of fitted parameters forms a calibrated basis to study
dilute aqueous solutions. There have been other treatments of liquid water [8,15,16], which also
depend on the assumption of hydrogen-bonded clusters of larger size and 3D structure which are
successful in predicting properties, so the concept of molecular clusters in liquids has support from
other research. As pointed out by Kier [12], this model fulfills the hypothesis of Haggis [16]
regarding the properties of water being due to fractional amounts of clusters of various size. A
conclusion for undergraduate students is that relatively simple models of liquids can lead to results
which correlate with physical properties. However, the dynamic nature of molecules in the liquid
state does not lead to simple formulas. Dynamic models can provide a better understanding of the
nature of liquid structures.

SUMMARY
In this chapter, we have briefly treated chemical equilibria in a quantitative way using Gibbs’ free
energy concept G ¼ H TS and the concept of chemical potential for closed systems as
0
m(T, P) ¼ m þ RT ln P. Probably the most important aspect of the chapter was the derivation

P 2 DH vap 1 1
and use of the Clausius–Clapeyron equation ln ¼ applied to the boiling of
P 1 R T 2 T 1
liquids and to the triple point of a phase diagram for iodine relative to fingerprint enhancement. We
TVa 2
showing it is small but nonzero and less than
b
then developed the general case of (C p C V ) ¼
R for liquids. Open systems were encountered in which partial molal volumes of materials adjust
their volumes in the presence of one another. Open systems also need added terms for the chemical

qG
i
potential m ¼ but we consider only the ‘‘essential’’ closed systems. An example of
qn i
T, P, n j6¼i
the use of the method of Cellular Automata (CA) modeling to simulate liquids was given to show
that the behavior of liquids is still an area of research.